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प्रश्न
A polyhedron has 20 faces and 12 vertices. Find the edges of the polyhedron.
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उत्तर
By using Euler’s formula for polyhedron,
F + V – E = 2 ...[Where, F = faces, V = vertices, E = edges]
Given, Faces (F) = 20, Vertices (V) = 12
⇒ 20 + 12 – E = 2
⇒ 32 – E = 2
⇒ E = 32 – 2
⇒ E = 30
Hence, the edges of the polyhedron are 30.
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संबंधित प्रश्न
Using Euler's formula, find the values of x, y, z.
| Faces | Vertices | Edges | |
| (i) | x | 15 | 20 |
| (ii) | 6 | y | 8 |
| (iii) | 14 | 26 | z |
Which of the following cannot be true for a polyhedron?
If the sum of number of vertices and faces in a polyhedron is 14, then the number of edges in that shape is ______.
Euler’s formula is true for all three-dimensional shapes.
Look at the shapes given below and state which of these are polyhedra using Euler’s formula.
Look at the shapes given below and state which of these are polyhedra using Euler’s formula.
Look at the shapes given below and state which of these are polyhedra using Euler’s formula.
Using Euler’s formula, find the value of unknown z in the following table.
| Faces | 9 |
| Vertices | z |
| Edges | 16 |
Using Euler’s formula, find the value of unknown p in the following table.
| Faces | p |
| Vertices | 6 |
| Edges | 12 |
Using Euler’s formula, find the value of unknown r in the following table.
| Faces | 8 |
| Vertices | 11 |
| Edges | r |
